The onset time of Fermi’s golden rule

Fermi’s golden rule describes the decay dynamics of unstable quantum systems coupled to a reservoir, and predicts a linear decay in time. Although it arises at relatively short times, the Fermi regime does not take hold in the earliest stages of the quantum dynamics. The standard criterion in the literature for the onset time of the Fermi regime is t F ∼ 1/Δ ω , with Δ ω the frequency interval around the resonant transition frequency ω 0 of the system, over which the coupling to the reservoir does not vary appreciably. In this work, this criterion is shown to be inappropriate in general for broadband reservoirs, where the reservoir coupling spectrum takes the form R ( ω ) ∝ ω η , and for which it is found that for η > 1, the onset time of the Fermi regime is given by t F ∝ ( ω X / ω 0 ) η −1 × 1/ ω 0 where ω X is the high-frequency cutoff of the reservoir. Therefore, the onset of the Fermi regime can take place at times orders of magnitude larger than those predicted by the standard criterion. This phenomenon is shown to be related to the excitation of the off-resonant frequencies of the reservoir at short times. For broadband reservoirs with η ≤ 1, and for narrowband reservoirs, it is shown that the standard criterion is correct.

Hypothetical control of postural sway

Quiet standing exhibits strongly intermittent variability that has inspired at least two interpretations. First, variability can be intermittent through the alternating engagement and disengagement of complementary control processes at distinct scales. A second and perhaps deeper way to interpret this intermittency is through the possibility that postural control depends on cascade-like interactions across many timescales at once, suggesting specific non-Gaussian distributional properties at different timescales. Multiscale probability density function (PDF) analysis shows that quiet standing on a stable surface exhibits a crossover from low, increasing non-Gaussianity (consistent with exponential distributions) at shorter timescales, reflecting inertial control, towards higher non-Gaussianity. Feedback-based control at medium to longer timescales yields a linear decrease that is characteristic of cascade dynamics. Destabilizing quiet standing with an unstable surface or closed eyes serves to attenuate inertial control and to elicit more of the feedback-based control over progressively shorter timescales. The result was to strengthen the appearance of the linear decay indicating cascade dynamics. Finally, both linear and nonlinear indices of postural sway also govern the relative strength of crossover or of linear decay, suggesting that tempering of non-Gaussianity across log-timescale is a function of both extrinsic constraints and endogenous postural control. These results provide new evidence that cascading interactions across longer timescales supporting postural corrections can even recruit shorter timescale processes with novel task constraints that can destabilize posture.

Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation

We consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan–Moore–Gibson–Thompson (JMGT) equation arising in acoustics as an alternative model to the well-known Kuznetsov equation. We show a local existence result in appropriate function spaces, and, using the energy method together with a bootstrap argument, we prove a global existence result for small data, without using the linear decay. Finally, polynomial decay rates in time for a norm related to the solution will be obtained.

7-T MRI tracking of mesenchymal stromal cells after lung injection in a rat model

Background Mesenchymal stromal cells (MSCs) are able to migrate and engraft at sites of inflammation, injuries, and tumours, but little is known about their fate after local injection. The purpose of this study is to perform MSC tracking, combining in vivo 7-T magnetic resonance imaging (MRI) and histological assessment, following lung injection in a rat model. Methods Five lungs were injected with ferumoxide-labelled MSCs and five with perfluorocarbon-labelled MSCs and underwent 7-T MRI. MRI acquisitions were recorded immediately (T0), at 24 h (T24) and/or 48 h (T48) after injection. For each rat, labelled cells were assessed in the main organs by MRI. Target organs were harvested under sterile conditions from rats sacrificed 0, 24, or 48 h after injection and fixed for histological analysis via confocal and structured illumination microscopy. Results Ferumoxide-labelled MSCs were not detectable in the lungs, whereas they were not visible in the distant sites. Perfluorocarbon-labelled MSCs were seen in 5/5 injected lungs at T0, in 1/2 at T24, and in 1/3 at T48. The fluorine signal in the liver was seen in 3/5 at T0, in 1/2 at T24, and in 2/3 at T48. Post-mortem histology confirmed the presence of MSCs in the injected lung. Conclusions Ferumoxide-labelled cells were not seen at distant sites; a linear decay of injected perfluorocarbon-labelled MSCs was observed at T0, T24, and T48 in the lung. In more than half of the experiments, perfluorocarbon-labelled MSCs scattering to the liver was observed, with a similar decay over time as observed in the lung.

A Predictive Model for the Evolution of COVID-19

We predict the evolution of the COVID-19 pandemic in several countries by using a regression-based predictive model. In particular, the growth rate of the infection has been fitted as an exponential decay, as compared to a linear decay, reported previously. The model has been validated with the data of China and South Korea, where the pandemic is nearing to its end. The data of Italy, Germany, Spain, and Sweden show that the peak of the infection has reached i.e. a time when the new infections will start to decrease as compared to the previous day. The model predicts the approximate number of total infections at the end of the outbreak. The model prediction of the USA, and Brazil show that the peak will reach in the next two-three weeks. The total number of infections in the USA is estimated to be around 4 million by the model. The reported data of India show the start of disease evolution, with a large initial scatter in the growth rate. The possible peak date and the total number of infections are predicted using the data available.

Decay Management Model for Perishable Goods

Inventory management becomes a challenge when it comes to perishable goods. In practice managing perishable goodsis a difficult task worldwide.Improvement of inventory control of perishable goods depends on the model chosen or implemented. This paper proposes how to improve the profit and to reduce the risk of spoiling the goods with respect to the rate of decay which may be fixed or variable. By considering a specific type of perishable goods this experimental investigation has been done based on linear decay and exponential decay. It has been observed that irrespective of the type of decay, the energy level in forward approach is far better than the back approach of consuming the perishable goods.

A semi-analytical approach to the elastic loading behaviour of rough surfaces

The elastic loading behaviour of rough surfaces is derived based on the physical understanding of the contact phenomena, where the pressure distribution is analytically obtained without any negative values or convergence problems, thus the evolution of the contact behaviour is obtained in a semi-analytical manner. Numerical results obtained by the proposed approach facilitate the understanding of the contact behaviour in the following aspects: 1) the ratio of contact area to load decreases with an increase in real contact area; 2) normal approach-load relationship is approximated by an exponential decay under relatively small loads and a linear decay under relatively large loads; and 3) average gap shows an exponential relationship with load only in moderate load range.